\documentclass[11pt]{amsart}
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\usepackage{amssymb}
\usepackage{amsmath}
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\begin{document}

\section{Simulator}

\begin{eqnarray}
\dot{\mathbf{x}} &=& f(t, \mathbf{x}, \mathbf{u}) \\
\mathbf{y} &=& h(t, \mathbf{x}, \mathbf{u})
\end{eqnarray}

\begin{equation}
\mathbf{x}_{\mathrm{wing}} = [\vec{x}_g, \vec{v}_b, \vec{q}, \vec{\omega}]^T
\end{equation}

\begin{equation}
\mathbf{u}_{\mathrm{wing}} = [\vec{v}_{\mathrm{wind}}, \vec{\delta}, \vec{f}_{\mathrm{ext.}}]^T
\end{equation}

\begin{equation}
\mathbf{y}_{\mathrm{wing}} = [\phi, \theta, \psi]^T
\end{equation}

\begin{eqnarray}
\mathbf{x}_{n+1} &=& f(\mathbf{x}_n, \mathbf{u}_n) \\
\mathbf{y}_{n+1} &=& h(\mathbf{x}_n, \mathbf{u}_n)
\end{eqnarray}


\section{Wind}

\begin{equation}
v(h) = v_0 \left( \frac{h}{h_0} \right)^{\alpha}
\end{equation}



\end{document}
